Problem: Solve for $x$ and $y$ using elimination. ${-2x+6y = 16}$ ${-x+5y = 18}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-2x+6y = 16}$ $2x-10y = -36$ Add the top and bottom equations together. $-4y = -20$ $\dfrac{-4y}{{-4}} = \dfrac{-20}{{-4}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {-2x+6y = 16}\thinspace$ to find $x$ ${-2x + 6}{(5)}{= 16}$ $-2x+30 = 16$ $-2x+30{-30} = 16{-30}$ $-2x = -14$ $\dfrac{-2x}{{-2}} = \dfrac{-14}{{-2}}$ ${x = 7}$ You can also plug ${y = 5}$ into $\thinspace {-x+5y = 18}\thinspace$ and get the same answer for $x$ : ${-x + 5}{(5)}{= 18}$ ${x = 7}$